First thing’s first. You need to download yourself the emulators you want. If you are using a Mac, look no further than OpenEmu. If you are on Windows I am afraid I can’t be of much help.
8 and 16 Bit Consoles
This includes consoles and handhelds like Sega Master System, Genesis, NES, SNES, Turbo Grafx 16, Gameboy, Gameboy Advanced and a few others.
There is nothing hard about playing these roms. You can simply google “Whatever NES Rom Download” and get the file. You will probably be directed to Romnation, Coolrom or Emuparadise. Those sites are fine, although if you want to save yourself a bunch of trouble you might want to download the No-Intro collection from Archive.org (https://archive.org/details/No-Intro-Collection_2013-06-14). You can download the whole torrent file, or browse the collection and download the specific titles you want.
If you are dealing with roms from sources other than the No-Intro-Collection you probably want to make sure to get roms that have the suffix (U) for United States and (!) for verified good. Sometimes it’s fun to dabble in (E) European games as some of them never saw US release.
MAME roms (arcade games) are a special case. Before you can play many of the games you need to download and install some device roms and bios files. Think of these as circuit boards you need to install. Namco games like Pac Man, for example, require the Namco boards to be installed in your “machine.” NeoGeo games like Metal Slug require the NeoGeo hardware. Here are all the bios I currently have installed:
That is not an comprehensive list, but I have been trying tons of games so this is a good start. Search for those, download them and drag them.
If a game doesn’t work, chances are it’s because you are missing one or more of these bios files. Figuring out what you need might take some googling.
If you are on Mac and using OpenEmu, you can use Console.app to determine what it is. Just open Console, open the rom that doesn’t work and read the error message. Here is a message I generated as an example trying to play Battle Toads without the right bios installed:
OpenEmuHelperApp: MAME: Audit failed with output:
btoads : bsmt2000.bin (8192 bytes) – NOT FOUND (bsmt2000)
As you can see, bsmt2000.bin was not found. Once bsmt2000 is installed the game will run no problem.
I don’t know how or what is going on from a legal standpoint but Archive.org just has every game. You can download every MAME rom in a huge 42GB file, or you can browse the collection using this link:
Once there, you can just search for any ROM you want. Make sure to download all of the bios files listen above. MAME roms don’t always have obvious names. If you are having trouble figuring out what to download search for your game on MameDB to figure out it’s filename. For example the game Battle Cross is called battlex.zip.
Playstation is another special case that requires bios files to run. You will need to download and install: scph5500.bin, scph5501.bin and scph5502.bin. The last one is pretty hard to find (I never could get one that works) but you can instead download scph5552.bin and rename it scph5502.bin and it seems to be the same. Here is the official page of required bios files.
I would link to them to make it easy for you but the links for these things are kinda … sketchy. They are often down, look disgusting, or unreliable so it might take you a bit of effort to find reliable downloads. The good news is once you get them installed, PSX emulation is pretty much flawless.
When you download a PSX game you will need to unzip it. Inside that folder is probably going to be one .cue file and one or a bunch of .bin files. You only need to drag the .cue file into OpenEmu and the PSX game should show up.
Have fun exploring all the games you might have missed, and replaying all your childhood favorites. There are many other games and other systems out there and some require some hoop jumping and I am not equipped to write guides for them all. If you want to dig deeper you can try asking me, but i can’t be sure I can help.